Multi-layer finite element method for modeling of package power and ground planes

Abstract

In a method for simulating electrical characteristics of a plurality of power planes, each power plane includes a plurality of geometric features. The geometric features of each power plane are projected onto a single planar construct. A polygonal mesh, including a plurality of pairs of interconnected nodes, that corresponds to the single planar construct is generated. The polygonal mesh is projected onto at least one power plane an equivalent circuit between each adjacent node of the plurality of interconnected nodes is projected onto the power plane. An equivalent capacitance is assigned between each node and a common ground planer. A finite element equation that includes a plurality of discrete terms is generated. The equation is solved, thereby determining the electrical characteristic value between each pair of adjacent nodes.

1. A method, operable on a digital computer coupled to a user interface, for simulating electrical characteristics of a plurality of power planes, each power plane including a plurality of geometric features, comprising the actions of:
 a. projecting the geometric features of each power plane onto a single planar construct; 
 b. generating a polygonal mesh, including a plurality of pairs of interconnected nodes, that corresponds to the single planar construct; 
 c. projecting the polygonal mesh onto at least one power plane of the plurality of power planes and generating an equivalent circuit between each adjacent node of the plurality of interconnected nodes projected onto the at least one power plane, thereby generating a plurality of equivalent circuits, each of the plurality of equivalent circuits describing an electrical characteristic of the at least one power plane in a region between each pair of adjacent nodes; 
 d. assigning an equivalent capacitance between each node and a common ground plane; 
 e. generating a finite element equation that includes a plurality of discrete terms, wherein each discrete term describes a different one of the plurality of equivalent circuits; 
 f. solving the finite element equation so as to determine the electrical characteristic value between each pair of adjacent nodes in relation to an initial electrical property of the at least one power plane; and 
 g. generating a human-perceptible indication of the electrical characteristic value between each pair of adjacent nodes of the at least one power plane. 
 
     
     
       2. The method of  claim 1 , wherein the action of generating an equation comprises generating a matrix equation that includes each discrete term in an arrangement corresponding to a spatial arrangement of each of the nodes. 
     
     
       3. The method of  claim 1 , wherein the action of generating a polygonal mesh comprises generating a triangular mesh. 
     
     
       4. The method of  claim 3 , wherein the triangular mesh comprises generating a Delaunay mesh. 
     
     
       5. The method of  claim 1 , wherein each equivalent circuit comprises an impedance value. 
     
     
       6. The method of  claim 5 , wherein the impedance value includes a capacitive component and an inductive component. 
     
     
       7. The method of  claim 1 , wherein the action of generating a polygonal mesh comprises generating a non-uniform triangular mesh in which the nodes are relatively less dense in areas of the planar construct that are relatively more homogeneous electrically and in which the nodes are relatively more dense in areas of the planar construct that are relatively less homogeneous electrically. 
     
     
       8. The method of  claim 1 , wherein the action of solving the finite element equation comprises the action of approximating a Helmholtz equation solution. 
     
     
       9. A system configured to simulate electrical characteristics of a plurality of power planes, each power plane including a plurality of geometric features, the system comprising:
 a digital computer coupled to a user interface and a memory, the memory storing program instructions executable by the digital computer to: 
 a. project the geometric features of each power plane onto a single planar construct; 
 b. generate a triangular mesh, including a plurality of pairs of interconnected nodes, that corresponds to the single planar construct; 
 c. project the triangular mesh onto at least one power plane of the plurality of power planes and configured to generate an equivalent circuit between each adjacent node of the plurality of interconnected nodes projected onto the at least one power plane, thereby generating a plurality of equivalent circuits, each of the plurality of equivalent circuits describing an electrical characteristic of the at least one power plane in a region between each pair of adjacent nodes; 
 d. assign an equivalent capacitance between each node and a common ground plane; 
 e. generate a finite element equation that includes a plurality of discrete terms, wherein each discrete term describes a different one of the plurality of equivalent circuits; 
 f. solve the finite element equation so as to determine the electrical characteristic value between each pair of adjacent nodes in relation to an initial electrical property of the at least one power plane; and 
 g. using the user interface, generate a human-perceptible indication of the electrical characteristic value between each pair of adjacent nodes of the at least one power plane. 
 
     
     
       10. The system of  claim 9 , wherein the equation comprises a matrix equation that includes each discrete term in an arrangement corresponding to a spatial arrangement of each of the nodes. 
     
     
       11. The computer of  claim 9 , wherein the triangular mesh comprises a Delaunay mesh. 
     
     
       12. The computer of  claim 9 , wherein each equivalent circuit comprises an impedance value. 
     
     
       13. The computer of  claim 12 , wherein the impedance value includes a capacitive component and an inductive component. 
     
     
       14. The computer of  claim 9 , wherein the triangular mesh comprises a non-uniform triangular mesh in which the nodes are relatively less dense in areas of the planar construct that are relatively more homogeneous electrically and in which the nodes are relatively more dense in areas of the planar construct that are relatively less homogeneous electrically. 
     
     
       15. The computer of  claim 9 , wherein solving the finite element equation comprises approximating a Helmholtz equation solution.